Hello @user1075​ - that's an interesting question and something I see can be useful.

I was checking on my Intercom environment and there are no options in Inbox Automation Rules to check for the priority of the conversation.

Actually, I think that marking priority is not an attribute/tag of the conversation generally so it can not be used in any rules.

The workaround would be to manually set the conversation attribute (note: conversation tag can be set but not used in these rules!). And then you need to remove it / change it manually again. This is not something that is easy to do from within Intercom, you can not just go and edit attributes.